Question

An electronics store uses a fixed order quantity inventory control system. Characteristics of one of its items is as follows: weekly demand is 2,000 units, ordering cost is $35 per order, holding cost per week is $0.04, replenishment lead-time is 3 weeks and the standard deviation of weekly demand is 400 units. Assuming the store operates 50 weeks per year, what is the EOQ for this item? Calculate the reorder point with safety stock if the store wishes to provide a 90 percent cycle-service level.

Answer 1

Following data have been provided :

Annual demand = D = 2000 / week x 52 weeks = 104000 units

Ordering cost = Co = $35 / order

Annual unit holding cost = Ch = $0.04 / week x 52 weeks = $2.08

EOQ for this item

= Square root ( 2 x Co x D / Ch )

= Square root ( 2 x 35 x 104000 /2.08 )

= 1870.82 ( 1871 rounded to nearest whole number )

EOQ = 1871 units

Standard deviation of weekly demand = 400 weeks

Lead time = 3 weeks

Therefore , Standard deviation of demand during lead time = 400 x Square root ( Lead time ) = 400 x Square root ( 3 )= 400 x 1.732 = 692.80

Z Value for 90 percent service level = NORMSINV ( 0.90 ) = 1.2815

Therefore , safety stock = Z value x Standard deviation of demand during lead time= 1.2815 x 692.80 = 887.82 ( 888 units rounded to nearest whole number )

Reorder point = Weekly demand x Lead time ( weeks ) + safety stock = 2000 x 3 + 888 = 6000 + 888 = 6888 units

REORDER POINT = 6888 UNITS

SAFETY STOCK = 888 UNITS